Assessing Horizontal Force Production in Resisted Sprinting:
Computation and Practical Interpretation
Matt R. Cross, Farhan Tinwala, Seth Lenetsky, Scott R. Brown, Matt Brughelli,
Jean-Benoit Morin, and Pierre Samozino
The assessment of horizontal force during overground sprinting is increasingly prevalent in practice and research, stemming from
advances in technology and access to simpliﬁed yet valid ﬁeld methods. As researchers search out optimal means of targeting the
development of horizontal force, there is considerable interest in the effectiveness of external resistance. Increasing attention in
research provides more information surrounding the biomechanics of sprinting in general and insight into the potential methods of
developing determinant capacities. However, there is a general lack of consensus on the assessment and computation of horizontal
force under resistance, which has resulted in a confusing narrative surrounding the practical applicability of loading parameters for
performance enhancement. As such, the aim of this commentary was twofold: to provide a clear narrative of the assessment and
computation of horizontal force in resisted sprinting and to clarify and discuss the impact of methodological approaches to
subsequent training implementation. Horizontal force computation during resisted sleds, a common sprint-training apparatus in the
ﬁeld, is used as a test case to illustrate the risks associated with substandard methodological practices and improperly accounting for
the effects of friction. A practical and operational synthesis is provided to help guide researchers and practitioners in selecting
appropriate resistance methods. Finally, an outline of future challenges is presented to aid the development of these approaches.
Keywords:sprint training, heavy sled, system mass, friction coefﬁcient, kinetics, ground-reaction force, power
A key physical determinant of many sports is the ability to
express force at a range of movement velocities.
acceleration, assessing the component of ground-reaction force
applied in the direction of the sprint (ie, horizontal force [F
help further our understanding of performance. As such, there is
considerable interest in assessing F
with applications in monitoring
as well as the selection of training parameters.
One area of interest is assessing F
while sprinting against
resistance to better understand the kinetic impact of potential
training regimes. Unfortunately, measuring F
sprinting (eg, towing a sled or using a winch device) is somewhat
complex, and ensuring accurate and consistent measurement and
computation is crucial. The aim for this commentary is to provide a
clear narrative of the assessment and computation of horizontal
force in resisted sprinting, and to critically discuss the impact of
methodological approach on training applicability.
Interplay of Mechanics
During Sprinting Acceleration
During sprinting acceleration, the force produced by muscle aims
to overcome inertia and any friction forces. The greater the force
(in this case F
) expressed, the greater the acceleration for a given
system mass (body mass plus any additional load; see Table 1).
Any external resisting forces impede acceleration for a given
output and must be overcome if the athlete is to accelerate.
In a typical sprint, no resistive forces are present except air friction
), which increases with the square of velocity (ie, high at
the end of the acceleration phase).
In resisted sprinting, both
inertia and resistive force can be manipulated.
In a resisted sprint, the same principles can be applied in the
horizontal direction as unresisted sprinting.
The main differences
are that (1) system inertia typically increases (eg, resisted sleds)
and, with it, the force required to accelerate, and (2) additional
resistive forces are present—the magnitude and manner of which
are method dependent (commonly sliding friction force); practi-
cally, the result is less acceleration and a lower peak velocity
attained per unit of F
. However, while system inertia is simple,
computing resistive force is more complex.
Measurement and Computation
of Horizontal Force
Measurement techniques fall into two categories: direct and indi-
rect. The former involves the direct assessment of ground reaction
forces using force platforms embedded under the running surface
(typically in the ground
or under a treadmill belt
). From this point,
can be separated from the resultant ground reaction force vector.
can also be indirectly estimated using a strain gauge attached
between the athlete and a ﬁxed point, or resistive device.
case, the raw output is an “offset force,”which makes it difﬁcult to
precisely estimate F
speciﬁc to ground contact (a limitation of
various force treadmills
). Other indirect methods estimate net F
production over time by utilizing an inverse dynamic approach
applied to the center of mass.
The approach requires only velocity
Cross and Samozino are with the Interuniversity Laboratory of Biology of Motricity,
Savoie Mont Blanc University, Chambéry, France. Cross is with the Scientiﬁc and
Sports Dept, Fédération Française de Ski, Annecy, France. Cross, Tinwala, Le-
netsky, Brown, Brughelli, and Morin are with the Sports Performance Research Inst
New Zealand (SPRINZ), Auckland University of Technology, Auckland, New
Zealand. Brown is with Neuromuscular and Rehabilitation Robotics Laboratory
(NeuRRo Lab), Dept of Physical Medicine and Rehabilitation, University of
Michigan Medical School, Ann Arbor, MI. Morin is with the Côte d’Azur
University, LAMHESS, Nice, France. Cross (firstname.lastname@example.org) is
International Journal of Sports Physiology and Performance, (Ahead of Print)
© 2019 Human Kinetics, Inc. INVITED COMMENTARY
or distance–time measurements and has been used on data from a
variety of devices (eg, global positioning systems,
and high-speed cameras
While the former direct approach can provide insight into the
speciﬁc events occurring, the advantage of the latter indirect
approach is that it can more easily be integrated into the ﬁeld.
The effects of resistance on F
can certainly be measured using
direct approaches (typically treadmills
or single foot strikes
), but it is for reasons of practicality that indirect
approaches have attracted interest.
Methods of Manipulating F
Resistance in Sprinting
There are four main methods of providing horizontal resistance
to an athlete: aerodynamic (eg, parachutes), motorized (otherwise
termed “robotic;”eg, 1080 Sprint; 1080 Motion, Austin, TX),
pulley (eg, Exergenie, Thousand Oaks, CA), and sliding (eg, sleds
or equivalent). While not well examined, aerodynamic resistance
should adhere to the same drag computations published on the
human body (ie, F
; permitted shape and drag factor are known).
Contemporary motorized devices provide resistance via measured
increments of torque via a servo motor.
Force production will
typically be computed as a product of simulated inertia, resistive
value of braking, and acceleration via rotary encoder. Pulley
devices provide resistance in the form of friction applied to a
drum or directly to a cable in more simple devices, and do not
substantially increase the inertia of the system. However, the
magnitude and consistency of resistance provided per increment
of braking must be experimentally determined. Sliding devices
move with the athlete, and consequently increase system inertia.
Additional resistive force is also present from the sliding of the
device over the ground (ie, friction force [F
In its simplest form, F
can be estimated using a basic
conversion factor (“coefﬁcient of friction;”μ
experimentally means approximated based on known values
(eg, normative data on the coefﬁcient between metal and grass).
represents the conversion between the normal force the sled load
applies to the ground (ie, the sled + additional load under gravity)
and the resulting horizontal F
applied to the athlete. For example,
if sled sprinting with a sled mass of 40 kg and a μ
of 0.3, F
be approximately ∼128 N. μ
can change depending on the surface
device characteristics, magnitude of normal loading, environmen-
tal characteristics, and even movement velocity.
One can estimate
using a common handheld “baggage”scale to directly measure
the friction force across a range of masses by pulling at a constant
speed (ﬁtting a linear regression between pulling force and normal
however, substantially more complex methods might be
necessary to provide accurate results.
Interested parties are
encouraged to read further.
At present, resisted sleds are probably the most commonly
used external horizontal overload,
and for this reason (and their
relative computational complexity), we will use this method to
focus the following discussion.
From Inaccurate Computation
A clear problem in the literature is a lack of narrative regarding the
type and magnitude of resistive forces (generally, friction) provided
by resistance modalities and, consequently, how this is factored into
computations of total output. Notably, a recent meta-analysis
classiﬁed loading solely on the additional normal load (% body
mass), and while surface “types”were reported (eg, “rigid”), this
rudimental categorization does not displace or accurately represent
friction characteristics. The overarching problem is that, for a given
load, the resistance experienced by the athlete could change sub-
stantially (eg, doubled or halved
) purely as a product of
To illustrate the problem with a lack of consensus of approach,
we will compare methods of two studies
indirect, external F
using resisted sleds. Both studies aimed to
compute the optimal loading for maximizing horizontal power, and
were published in quick succession, but provided markedly differ-
ent results and conclusions. The ﬁrst is a study by Cross et al
in which F
was computed at peak velocity (an approach justiﬁed
and discussed at length
) following a friction experiment.
second is a study by Monte et al,
who computed F
the acceleration phase of each sprint while noting kinematic
The base computations (per unresisted sprinting) used in both
studies are identical, but they differ in accounting for resistance due
to external loading. Cross et al
by increasing the
total inertia of the system per the mass of the sled and harness, and
Table 1 Nomenclature, Basic Deﬁnitions, Measurement, and Computational Background of Horizontal Force
Definition Measurement and calculation
Portion of the ground-reaction
force acting in the sprint direction
Measured directly at the point of application using force platforms. Otherwise, estimated as
the product of its determinant variables.
Acceleration occurring in the
direction of the sprint
Determined as rate of change in velocity with respect to time. Can be measured via a wide
variety of technologies to various degrees of accuracy.
mTotal system mass Measured using a simple summation of all mass included in the system being accelerated
(eg, body mass, vest, loaded sled).
Aerodynamic friction force Estimated using published equations, from a combination of athlete characteristics (mass
and height, converted to frontal area), environmental characteristics (temperature, wind
speed, and pressure), and instantaneous velocity.
Friction force Estimated using experimentation or published equations. Magnitude is determined by the
application of braking or loading, converted to effective resistance using a coefﬁcient of
friction. The coefﬁcient may not be consistent and can change based on loading and/or
velocity. Final value may require correction for angle of pulling (which itself can be
measured directly or estimated from standing height and tether length).
Base computation: Fh=m·ahþFaero þFf:
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2Cross et al
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as a constant (per F
was computed using a sled
load and an experimentally conﬁrmed μ
, which varied based on
velocity (via a polynomial ﬁt).
The angle between the ground and
tether was also calculated to help separate the horizontal ground
reaction force component from any vertical occurring. Monte
did not directly compute friction force, but considered
the additional resistance as an equivalent load experienced by
the athlete. To “correct”for the effects of friction, the initial
prescription of each sled mass was reduced by the magnitude of
friction–equivalent loading using an experimentally determined μ
of 0.2 (eg, original mass = 10 kg, equivalent loading = 2 kg, ﬁnal
mass prescribed = 8 kg). In this manner, it appears that the authors
believed that the effects of friction force were completely accounted
for, although it remains unclear if the reduced or original load was
used in F
computations. Clearly, correcting for “horizontal load-
ing”by subtracting its raw magnitude from that applied vertically is
problematic, since F
is a product of the total normal load of the sled
and environmental characteristics (eg, ∼1.6-kg-equivalent loading is
still experienced for a “corrected”8-kg sled mass).
The method presented by Monte et al
may result in substan-
tial inaccuracies in the force produced to overcome inertia during
acceleration (considered mass may differ from that experienced)
and an underestimation of friction forces (notably in late sprint
phases). To facilitate understanding, Figure 1displays the effects of
this method on computed F
during sprinting acceleration with two
loads. Notably, the limitations of this method are perhaps most
apparent in conditions nearing zero acceleration (eg, peak or
maintained velocity), since the force to overcome sled friction is
“corrected”for in an artiﬁcial inertia. Consequently, the computa-
tion assumes at constant velocity the only net F
being produced is
to overcome F
. To emphasize, regardless of whether the sled
load is 5 kg or 100 kg, the force produced by the athlete during
constant velocity is assumed to be only due to air.
Implications for Training
output during resisted sprinting is regularly presented as a
means of understanding the value of potential training parame-
; the examples earlier illustrate how methodological prob-
lems can directly affect the results on which such judgments are
made. Similarly, the methods through which mechanical parame-
ters are measured and computed need to be associated with a clear
narrative around their speciﬁc applicability.
Figure 1 —Illustration of the differences in external maximal power in the horizontal direction over the course of 2 sprints, with (black line) and
without (gray line) accounting for the constant variable of friction force, applied to the instantaneous velocity–time data of athletes sprinting with 2
different loading protocols: (A) 20% body-mass load (chosen to be representative of the highest loading protocol used by Monte et al
) and (B) 79%
body-mass load (corresponding to approximately the mean load maximizing power in Cross et al
). Black line indicates computation accounting for the
effects of friction force as a constant
; gray line, correction computation used by Monte et al.
Both examples are based on the same calculation of
inertia, on a Mondo track surface, coefﬁcient of friction = ∼0.4.
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Horizontal Force in Resisted Sprinting 3
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Commonly, measurement occurs under a selection of external
protocols, after which instantaneous or average F
compared with gain insight into which parameters acutely enhance
output (eg, maximizes force or power). However, the nature of such
measurement and computation may be problematic for those
expecting beneﬁcial training outcomes. As an example, if training
resistance is selected based on instantaneous maximization during
an athlete will similarly spend only a single instant
in these “targeted conditions”per acceleration performed. The
minimal cumulated time spent in targeted conditions per training
block might limit practical beneﬁt and could partially explain the
typically similar adaptations experienced in resisted versus unre-
sisted sprinting interventions.
A clear solution to increasing exposure is to ﬁnd the load that
allows targeted conditions to be reached at the peak velocity plateau,
since this is the only velocity that can be maintained over several
seconds of maximal exercise (fatigue permitting).
est in this approach is that if resistance is selected to target the
development of a given level of F
at peak velocity, the athlete can
spend an extended period (eg, 3–5 s per sprint) near these optimized
conditions by simply attaining and maintaining peak velocity. The
practical consequence is greater time spent in targeted conditions
than other approaches (see Figure 2for an example of targeting
maximum power). Nevertheless, the method has limitations; namely,
it ignores the work performed (and fatigue induced) between the start
and reaching peak velocity. An alternative approach might be the
assessment of loading parameters based on the average output over a
distinct period (eg, 10 m). Certainly, this is a valuable avenue for
Distinct bands of velocity can be targeted by ﬁxing a speciﬁc
training load, and these conditions are likely relevant to unloaded
While some may argue that loading selected in this
manner ignores technical speciﬁcity because it aims to recreate
the conditions experienced during a speciﬁc moment of the acceler-
ation phase, it follows that kinematic conditions might be similar
when compared in this manner (eg, the instant of 5 m·s
acceleration vs 5 m·s
peak resisted velocity). These similarities (or
indeed dissimilarities) require clariﬁcation, but do not necessarily
degrade the possibility of longitudinal improvement in determinant
physical capabilities as part of a balanced periodization. Neverthe-
less, the actual effects of training using stimuli selected for its kinetic
speciﬁcity remain unclear,
and more research is needed.
We encourage researchers to utilize the measurement of F
resisted sprinting but to carefully consider the impact of study
design and computation on their conclusions. Where possible,
Figure 2 —Graphic showing the differences in (A) power output and (B) F
over the course of 2 different loading protocols: unloaded sprinting (black
line) and 79% body-mass load (gray line). The computation of force for the resisted sprint follows the procedures described in detail elsewhere.
intended to exemplify the difference in time spent at a targeted kinetic output (in this example, maximum horizontal power), when assessed at maximum
resisted velocity compared with during the acceleration phase.
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4Cross et al
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experimentally determine friction coefﬁcients, or consider using an
“outcome”variable (eg, decrement in maximum velocity), to select
and classify loading parameters. Practitioners may use published
coefﬁcients to estimate outputs, while acknowledging substantial
errors may occur. Those wishing to use resisted sprinting to target
the development of distinct bands output might forgo F
ment and simply select loading based on velocity decrement.
Where training implications are valued as an outcome, researchers
are encouraged to carefully orient their study design and analysis to
maximize applicability to practice, or at least clearly discuss
limitations. Finally, the measurement and improvement of F
does not supplant a balanced approach to improving sprinting
performance and, therefore, should not be presented nor interpreted
as such by researchers and readers alike.
Rapidly developing technology has made F
for many practitioners. Assessing F
can provide valuable insight
into athlete capabilities, and can guide training when combined
with resisted sprinting. This progress is accompanied with a need
for careful implementation and computations. As such, researchers
must be attentive in their methodological proceedings and well
consider the practical applicability of their ﬁndings.
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Horizontal Force in Resisted Sprinting 5
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